Way to avoid two bookings for a flight?

I'm using DoHop to find flights but I notice that some of the best/cheapest flights for me require two bookings.

For example, I found the following:

This raises some questions for me:

• Why are 2 bookings required here?
• What are the dangers of 2 bookings?
• If I tell them at the first check-in I have a connecting flight, will they be likely to book me through anyways?
• Is there any "trick" to do one booking for a similar price?

I would prefer to have check-in luggage (though perhaps if answers are negative I can try to get myself a carry-on case).

Specifics of this case:

I'm not really worried about the outbound flight since, in the worst case, I have plenty of time to get my luggage, check in again, etc. However, the return flight looks tight for me, assuming I would have to get luggage, change terminals, and check in again. Would they really not check me through from Dublin to Santiago?

Updates:

The answers summarise that, on a double-booking, the airlines have no responsibility in the case of a missed connection due to a delayed flight, nor to check luggage through to the final destination. They offered some useful info but didn't really get to the heart of the matter.

In some cases, airlines will, however, check through luggage on separate tickets. Until 2016, Oneworld airlines (BA, Iberia, LATAM, etc.) did guarantee that they would check through luggage on other Oneworld flights with separate tickets assuming at least a 2 hour layover. However, in 2016 they removed that guarantee. This did not mean that airlines stopped doing it overnight, just that they were no longer forced to as part of the alliance agreement. Some airlines in the alliance went back and forward on that policy.

It seems, however, that Iberia do not (officially) check through luggage on separate tickets. In general, information is sketchy, however. Try check with your specific airline and whatever alliance they are part of if they have any policy in this regard.

I am still, however, completely clueless as to why these flights (all on Oneworld airlines) could not be combined into one booking by the system (or, seemingly, any other system: I tried various including those provided by the airlines themselves).

In the end I booked another flight on a competing airline with a similar schedule but for more money. I felt sort of happy to pay extra to avoid this idiocy having wasted enough time trying to understand something that makes no sense to me.